These studies investigate mathematical models of the immune network and the Kinetics of its many complex interacting components, viz. precursors, CD4+ helper T-lymphocytes, CD8+ cytotoxic T-lymphocytes, natural killer (NK) and lymphokine activated killer (LAK) monocytes, interleukins, and interferons by means of a system of nonlinearly coupled, ordinary differential equations. An appropriately constructed and validated network model should suggest experiments and theoretic rationale that can guide the use of therapeutic interventions and vaccines and promote understanding of how the immune system might be manipulated to increase its effectiveness in preventing or combating pathogenic infections. Current studies involve the interaction of the human immunodeficiency virus with CD4+ helper T-lymphocytes (T4 cells) in culture media. These simulation studies support the Zigury cytopathology model which postulates that each antigenic stimulation amplifies the presence of the infection by the conversion (activation) of large numbers of newly infected T4 cells; these T4 cells then express new virus, lyze, and die, but leave behind free virus that expands the infection of the precursor population. Thus, the T4 cell population is left in an increased state of infection after each occurrence of antigenic stimulation. The loss of infected T4 cells and precursors by viral destruction reduces the capacity of the immune system to respond to new antigens or antigens previously encountered. Current simulation studies attempt to deal with in vitro systems of cells and virus in culture media where data would be feasibly obtained by experiment. Hence these studies differ from other published simulation studies that have attempted to deal with the entire in vivo immune system and must make unrealistic assumptions about its character in order to reduce the considerable number of undetermined interaction coefficients.